Fourier Transform and Spectral Densities

This lecture covers the definition of the Fourier transform according to Risken, the concept of spectral densities, the gated Fourier transform for real signals limited in time, the Wiener-Khinchin theorem, and the Langevin equation for Brownian motion. It also discusses the two-force hypothesis, the Wiener increment, and Itō's lemma in stochastic processes.